/*Hotellings T2 data from Morrison - pg 154*/
/*These data are the same as Assignment #3*/
data hotel;
input y1 y2 y3 group;
cards;
1.21 .61 .70 1
.92 .43 .71 1
.80 .35 .71 1
.85 .48 .68 1
.98 .42 .71 1
1.15 .52 .72 1
1.10 .50 .75 1
1.02 .53 .70 1
1.18 .45 .70 1
1.09 .40 .69 1
1.40 .50 .71 2
1.17 .39 .69 2
1.23 .44 .70 2
1.19 .37 .72 2
1.38 .42 .71 2
1.17 .45 .70 2
1.31 .41 .70 2
1.30 .47 .67 2
1.22 .29 .68 2
1.00 .30 .70 2
1.12 .27 .72 2
1.09 .35 .73 2
;
proc glm; class group;
model y1 y2 y3 = group;
manova h=group;
run;
Hotelling's T2 Example 1
---------------------------------------------------------------------------------
General Linear Models Procedure
Class Level Information
Class Levels Values
GROUP 2 1 2
Number of observations in data set = 22
---------------------------------------------------------------------------------
Dependent Variable: Y1
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 0.18668182 0.18668182 11.27 0.0031
Error 20 0.33130000 0.01656500
Corrected Total 21 0.51798182
R-Square C.V. Root MSE Y1 Mean
0.360402 11.38068 0.12871 1.13091
Dependent Variable: Y1
Source DF Type I SS Mean Square F Value Pr > F
GROUP 1 0.18668182 0.18668182 11.27 0.0031
Source DF Type III SS Mean Square F Value Pr > F
GROUP 1 0.18668182 0.18668182 11.27 0.0031
---------------------------------------------------------------------------------
Dependent Variable: Y2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 0.03549333 0.03549333 6.40 0.0199
Error 20 0.11085667 0.00554283
Corrected Total 21 0.14635000
R-Square C.V. Root MSE Y2 Mean
0.242524 17.51770 0.07445 0.42500
Dependent Variable: Y2
Source DF Type I SS Mean Square F Value Pr > F
GROUP 1 0.03549333 0.03549333 6.40 0.0199
Source DF Type III SS Mean Square F Value Pr > F
GROUP 1 0.03549333 0.03549333 6.40 0.0199
---------------------------------------------------------------------------------
Dependent Variable: Y3
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 0.00011045 0.00011045 0.34 0.5645
Error 20 0.00643500 0.00032175
Corrected Total 21 0.00654545
R-Square C.V. Root MSE Y3 Mean
0.016875 2.545952 0.01794 0.70455
Dependent Variable: Y3
Source DF Type I SS Mean Square F Value Pr > F
GROUP 1 0.00011045 0.00011045 0.34 0.5645
Source DF Type III SS Mean Square F Value Pr > F
GROUP 1 0.00011045 0.00011045 0.34 0.5645
---------------------------------------------------------------------------------
General Linear Models Procedure
Multivariate Analysis of Variance
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
Y1 Y2 Y3
2.61710531 100.00 -2.15110857 3.53381589 2.14703155
0.00000000 0.00 0.21179716 -0.20293819 12.34507152
0.00000000 0.00 0.81860064 1.87736923 0.00000000
---------------------------------------------------------------------------------
General Linear Models Procedure
Multivariate Analysis of Variance
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall GROUP Effect
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
S=1 M=0.5 N=8
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.27646417 15.7026 3 18 0.0001
Pillai's Trace 0.72353583 15.7026 3 18 0.0001
Hotelling-Lawley Trace 2.61710531 15.7026 3 18 0.0001
Roy's Greatest Root 2.61710531 15.7026 3 18 0.0001